Function Transformations

Front

What is a vertical shift in function transformations?

Back

A vertical shift occurs when a function is moved up or down on the graph. For example, h(x) = f(x) + k shifts the graph of f(x) up by k units if k > 0 and down by k units if k < 0.

Front

What does the transformation h(x) = f(x + 3) represent?

Back

This transformation represents a horizontal shift of the function f(x) to the left by 3 units.

Front

What does the transformation h(x) = f(x - 2) represent?

Back

This transformation represents a horizontal shift of the function f(x) to the right by 2 units.

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, h(x) = af(x) where a > 1.

Front

What is a vertical compression in function transformations?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, h(x) = af(x) where 0 < a < 1.

Front

What is the effect of a negative sign in front of a function, such as h(x) = -f(x)?

Back

This transformation reflects the graph of the function f(x) across the x-axis.

Front

What is the effect of a negative sign inside the function, such as h(x) = f(-x)?

Back

This transformation reflects the graph of the function f(x) across the y-axis.

Front

What type of function is represented by the equation y = |x|?

Back

This is an absolute value function, which creates a V-shaped graph.

Front

What type of function is represented by the equation y = x^2?

Back

This is a quadratic function, which creates a parabolic graph.

Front

What type of function is represented by the equation y = mx + b?

Back

This is a linear function, which creates a straight line graph.